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Journal articles on the topic 'Linguistic Distance Measures'

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Published: 5 June 2025

Last updated: 16 July 2025

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Wichmann, Søren, Eric W. Holman, Dik Bakker, and Cecil H. Brown. "Evaluating linguistic distance measures." Physica A: Statistical Mechanics and its Applications 389, no. 17 (2010): 3632–39. http://dx.doi.org/10.1016/j.physa.2010.05.011.

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Leonishiya, A., and John Robinson. "Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method." Indian Journal Of Science And Technology 16, no. 33 (2023): 2653–62. http://dx.doi.org/10.17485/ijst/v16i33.640-icrsms.

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A, Leonishiya, and Robinson John. "Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method." Indian Journal of Science and Technology 16, no. 33 (2023): 2653–62. https://doi.org/10.17485/IJST/v16i33.640-icrsms.

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Abstract Objective: In this paper we propose various Linguistic Intuitionistic Fuzzy Distance Measures (LIFDMs) for Linguistic Intuitionistic Fuzzy Sets (LIFSs) which are then utilized in the Linguistic Intuitionistic Fuzzy-Technique of Order Preference by Similarity to Ideal Solution (LIF-TOPSIS) method of Decision Support Systems (DSS). Methods: Some novel distance measures including membership, non-membership degrees and the linguistic index and distance measures based on Hausdorff metric are proposed in this work and related theorems are proved. Findings: The proposed distance measures are used to find the weights involved in the TOPSIS method. Numerical illustration is presented for the LIF-TOPSIS method and comparisons are made with existing ranking method and the ranking methods obtained from the different distance measures. The comparison study reveals the consistency of the ranking of the best alternative from the final ranking of the alternatives through the proposed distance measures. Novelty: Most of the researchers have done decision making with Linguistic Intuitionistic Fuzzy Sets, where the best alternatives are chosen using traditional distance measures involving only the intuitionistic fuzzy number or using some other calculations. In this paper we have proposed varieties of distance measures involving intuitionistic characterization and the linguistic characterization and proved that those distance measures are metrices. Using these different metrices we have derived different weight vectors for LIF-TOPSIS and the results give consistent decision for the discussed numerical illustration. Keywords: Linguistic Intuitionistic Fuzzy Sets (LIFSs); LIF-TOPSIS; Decision Support System (DSS); MAGDM; Linguistic Distance Measures

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Li, Wei, and Shouzhen Zeng. "Uncertain Linguistic Aggregation Distance Measures and Their Application to Group Decision Making." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/563650.

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We introduce a method based on distance measures for group decision making under uncertain linguistic environment. We develop some uncertain linguistic aggregation distance measures called the uncertain linguistic weighted distance (ULWD) measure, the uncertain linguistic ordered weighted distance (ULOWD) measure, and the uncertain linguistic hybrid weighted distance (ULHWD) measure. We study some of their characteristic, and we prove that the ULWD and the ULOWD are special cases of the ULHWD measure. Finally, we develop an application of the ULHWD measure in a group decision making problem concerning the evaluation of university faculty for tenure and promotion with uncertain linguistic information.

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Wu, Shuangsheng, Jie Lin, and Zhenyu Zhang. "New distance measures of hesitant fuzzy linguistic term sets." Physica Scripta 96, no. 1 (2020): 015002. http://dx.doi.org/10.1088/1402-4896/abc385.

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Meng, Fanyong, Yige Yuan, and Xiaohong Chen. "Several Generalized Interval-Valued 2-Tuple Linguistic Interval Distance Measures and Their Application." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 25, no. 05 (2017): 759–86. http://dx.doi.org/10.1142/s0218488517500337.

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Interval-valued linguistic variables are efficient tools to express the decision makers’ uncertain qualitative judgments. Considering the application of interval-valued linguistic variables, this paper proposes an interval distance measure, which is then used to define interval-valued linguistic interval distance measures by combining the 2-tuple linguistic representation model. To reflect the interactions between elements in a set, three correlative interval distance measures on intervalvalued linguistic variables are proposed. Meanwhile, several models designed to obtain the optimal weighting vector are constructed. After that, an approach to pattern recognition and to multi-attribute decision making with interval-valued linguistic information is developed. Meanwhile, associated examples are offered to demonstrate the concrete application of the proposed procedure.

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Yu, Guansheng, Shouzhen Zeng, and Chonghui Zhang. "Single-Valued Neutrosophic Linguistic-Induced Aggregation Distance Measures and Their Application in Investment Multiple Attribute Group Decision Making." Symmetry 12, no. 2 (2020): 207. http://dx.doi.org/10.3390/sym12020207.

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This paper studied the single-valued neutrosophic linguistic distance measures based on the induced aggregation method. Firstly, we proposed a single-valued neutrosophic linguistic-induced ordered weighted averaging distance (SVNLIOWAD) measure, which is a new extension of the existing distance measures based on the induced aggregation view. Then, based on the proposed SVNLIOWAD, a novel induced distance for single-valued neutrosophic linguistic sets, namely the single-valued neutrosophic linguistic weighted induced ordered weighted averaging distance (SVNLWIOWAD), was developed to eliminate the defects of the existing methods. The relationship between the two proposed distance measures was also explored. A multiple attribute group decision making (MAGDM) model was further presented based on the proposed SVNLWIOWAD measure. Finally, a numerical example concerning an investment selection problem was provided to demonstrate the usefulness of the proposed method under a single-valued neutrosophic linguistic environment and, then, a comparison analysis was carried out to verify the flexibility and effectiveness of the proposed work.

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Tan, Qian-Yun, Cui-Ping Wei, Qi Liu, and Xiang-Qian Feng. "The Hesitant Fuzzy Linguistic TOPSIS Method Based on Novel Information Measures." Asia-Pacific Journal of Operational Research 33, no. 05 (2016): 1650035. http://dx.doi.org/10.1142/s0217595916500354.

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Hesitant fuzzy linguistic term sets (HFLTSs) have attracted lots of attention recently due to their distinguished power and efficiency for dealing with multi-criteria decision making. To extend the applicability of HFLTSs, this paper first presents a more concise comparison formula of hesitant fuzzy linguistic term sets based on probability criterion of uniform distribution and develops novel distance measures considering the hesitance degree. Next, an aggregation scheme is designed to integrate OWD measure into the TOPSIS analysis procedure, in which we calculate different criterion weights according to the distance between criterion values and positive and negative ideal solutions. The weighted distances between the alternatives and positive and negative ideal solutions are calculated. Then the relative closeness degree to the positive ideal solution is calculated to rank all alternatives. Finally, an example is given to illustrate the capabilities and validation of the proposed algorithm.

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Wang, Juxiang, Jian Yuan, Jiajing Zhang, and Miao Tang. "A Novel Group Decision-Making Method Based on Generalized Distance Measures of PLTSs on E-Commerce Shopping." Complexity 2021 (June 9, 2021): 1–16. http://dx.doi.org/10.1155/2021/5553343.

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In multiattribute group decision-making (MAGDM), due to quantity, fuzziness, and complexity of evaluation linguistic information on commodities, traditional distance measures need to be extended to the integration of evaluation information under a multigranular probabilistic linguistic environment. A more reasonable method is proposed to deal with the missing value in the evaluation information. On the basis of the generalized distance measures and filling in the missing evaluation information, some novel distance measures between two multigranular probabilistic linguistic term sets (PLTSs) are presented in this paper. Based on these distance measures, three extended decision-making (DM) algorithms based on TOPSIS, the extended TOPSIS, and VIKOR are proposed, which are MGPL-TOPSIS, MGPL-ETOPSIS, and MGPL-VIKOR, respectively. The case analyses on purchasing a car are provided to illustrate the application of the extended multiattribute group decision-making (MAGDM) algorithms. Then, sensitivity analyses based on PT are proposed as well. In particular, the extended TOPSIS method is presented. These results demonstrate the novelty, feasibility, and rationality of the distance measures between two multigranular PLTSs proposed in this paper.

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Shan, Meng-Meng, Ping Li, and Hu-Chen Liu. "Interval 2-Tuple Linguistic Distance Operators and Their Applications to Supplier Evaluation and Selection." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/9893214.

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With respect to multicriteria supplier selection problems with interval 2-tuple linguistic information, a new decision making approach that uses distance measures is proposed. Motivated by the ordered weighted distance (OWD) measures, in this paper, we develop some interval 2-tuple linguistic distance operators such as the interval 2-tuple weighted distance (ITWD), the interval 2-tuple ordered weighted distance (ITOWD), and the interval 2-tuple hybrid weighted distance (ITHWD) operators. These aggregation operators are very useful for the treatment of input data in the form of interval 2-tuple linguistic variables. We study some desirable properties of the ITOWD operator and further generalize it by using the generalized and the quasi-arithmetic means. Finally, the new approach is utilized to complete a supplier selection study for an actual hospital from the healthcare industry.

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Kamacı, Hüseyin, Dragan Marinkovic, Subramanian Petchimuthu, Muhammad Riaz, and Shahzaib Ashraf. "Novel Distance-Measures-Based Extended TOPSIS Method under Linguistic Linear Diophantine Fuzzy Information." Symmetry 14, no. 10 (2022): 2140. http://dx.doi.org/10.3390/sym14102140.

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The advantages of the intuitionistic fuzzy set, Pythagorean fuzzy set, and q-rung orthopair fuzzy set are all carried over into the linear Diophantine fuzzy set by extending the restrictions on the grades. Linear Diophantine fuzzy sets offer a wide range of practical applications because the reference parameters allow evaluation andto express their judgments about membership and nonmembership degrees in a variety of ways. Linguistic-valued information cannot be described by linear Diophantine fuzzy numbers since precise numbers are used in linear Diophantine fuzzy systems. In this paper, we first present the novel idea of a linguistic linear Diophantine fuzzy set, which is the hybrid structure of the linear Diophantine fuzzy set and the linguistic term set. Furthermore, some basic operational rules with novel distance measures, namely, Hamming, Euclidean, and Chebyshev distance measures, are established. Based on the newly defined concept of distance measure, an extended TOPSIS technique is presented to tackle the linguistic uncertainty in real-world decision support problems. A numerical example is illustrated to support the applicability of the proposed methodology and to analyze symmetry of the optimal decision. A comparison analysis is constructed to show the symmetry, validity, and effectiveness of the proposed method over the existing decision support techniques.

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Zhao, Na, Zeshui Xu, and Zhiliang Ren. "Some Approaches to Constructing Distance Measures for Hesitant Fuzzy Linguistic Term Sets with Applications in Decision-Making." International Journal of Information Technology & Decision Making 17, no. 01 (2018): 103–32. http://dx.doi.org/10.1142/s0219622017500316.

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The purpose of this paper is to investigate the methods of constructing distance measures for hesitant fuzzy linguistic term sets (HFLTSs) and their applications in multi-criteria decision-making (MCDM). We first present some methods to construct distance measures for HFLTSs. Then, we discuss the properties of different distance measures in detail, which are very helpful in comparison of these distance measures for HFLTSs. After that, based upon the distance measures for HFLTSs, a decision-making method is proposed to solve the MCDM problems, in which the assessment values of alternatives over criteria are HFLTSs and the weights of criteria are completely unknown or expressed by HFLTSs. Finally, an example concerning the evaluation of movie quality is provided to demonstrate the practicability of the proposed method, and necessary comparative analyses are conducted to illustrate the effectiveness and advantages of the developed distance measures and the proposed decision-making method.

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Wu, Qun, Yimeng Wang, and Yuhan Wangzhu. "Connecting the Numerical Scale Model With Assessing Attitudes and its Application to Hesitant Fuzzy Linguistic Multi-attribute Decision Making." Journal of Operations Intelligence 3, no. 1 (2024): 17–45. http://dx.doi.org/10.31181/jopi31202531.

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The aim of this paper is to provide a specific numerical scale model with the purpose of making transformations between linguistic terms and numerical values. The proposed method represents a wide range of existing numerical scale models and can quantitatively reflect the linguistic behaviors of DMs. The pessimistic-optimistic principle based supplementary regulation for hesitant fuzzy linguistic term set (HFLTS) may lead to the initial information distortion and losing. On the basis of the lowest common multiple principle in number theory, an improved supplementary regulation is proposed to reserve the fidelity of original information, the improved supplementary regulation brings a new conception for information measures of HFLTS as well. Then based on the traditional generalized distance and Hausdorff distance measures, some new distance measures for HFLTS are presented in the numerical scale framework. Furthermore, an extended TOPSIS method for hesitant fuzzy linguistic MADM is developed. Finally, a numerical example concerning the preference of movies is elaborated on the performance of our approach. Sensitive and comparative analysis are also provided and discussed to show the effectiveness and advantages of the proposed method

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Wang, Jiefeng, Shouzhen Zeng, and Chonghui Zhang. "Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products." Mathematics 8, no. 3 (2020): 439. http://dx.doi.org/10.3390/math8030439.

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A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework.

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Lahiri, Rimita, Md Nasir, Manoj Kumar, et al. "Interpersonal synchrony across vocal and lexical modalities in interactions involving children with autism spectrum disorder." JASA Express Letters 2, no. 9 (2022): 095202. http://dx.doi.org/10.1121/10.0013421.

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Quantifying behavioral synchrony can inform clinical diagnosis, long-term monitoring, and individualised interventions in neuro-developmental disorders characterized by deficit in communication and social interaction, such as autism spectrum disorder. In this work, three different objective measures of interpersonal synchrony are evaluated across vocal and linguistic communication modalities. For vocal prosodic and spectral features, dynamic time warping distance and squared cosine distance of (feature-wise) complexity are used, and for lexical features, word mover's distance is applied to capture behavioral synchrony. It is shown that these interpersonal vocal and linguistic synchrony measures capture complementary information that helps in characterizing overall behavioral patterns.

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Cheng, Yali, Yonghong Li, and Jie Yang. "Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1147–60. http://dx.doi.org/10.3233/jifs-201429.

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Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

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Meng, Fanyong, and Xiaohong Chen. "A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures." Journal of Intelligent & Fuzzy Systems 28, no. 4 (2015): 1519–31. http://dx.doi.org/10.3233/ifs-141435.

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Cheng, Hao, Fanyong Meng, and Ke Chen. "Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application." International Journal of Fuzzy Systems 19, no. 4 (2016): 967–81. http://dx.doi.org/10.1007/s40815-016-0218-5.

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Zang, Yuqi, Xiaodong Zhao, Shiyong Li, and Adnan Nazir. "Grey Relational Bidirectional Projection Method for Multicriteria Decision Making with Hesitant Intuitionistic Fuzzy Linguistic Information." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/5691905.

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We investigate a novel approach for multicriteria decision making (MCDM) with hesitant intuitionistic fuzzy linguistic information. To compare the hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), we propose a comparison method of HIFLTSs. A family of distance measures of HIFLTSs is developed. After that, we propose the grey relational bidirectional projection method based on the proposed comparison method and distance measures of IVHFLNs for dealing with MCDM problems. Furthermore, we establish a nonlinear optimization model to obtain the weight vector of criteria. Finally, an illustrative example is given to demonstrate the effectiveness and flexibility of the proposed approach.

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Lu, Xueping, and Jun Ye. "Similarity Measures of Linguistic Cubic Hesitant Variables for Multiple Attribute Group Decision-Making." Information 10, no. 5 (2019): 168. http://dx.doi.org/10.3390/info10050168.

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A linguistic cubic hesitant variable (LCHV) is a hybrid form of linguistic values in group decision-making environments. It is composed of an interval language variable and multiple single-valued language variables given by different decision-makers (DMs). Due to the uncertainty and hesitation of DMs, the numbers of language variables in different LCHVs are unequal. Thus, the least common multiple number (LCMN) extension method was adopted. Based on the included angle and distance of two LCHVs, we presented two cosine similarity measures and developed a multiple attribute group decision-making (MAGDM) approach. An example of engineer selection was used to implement the proposed LCHV MAGDM method and demonstrate the simplicity and feasibility of the proposed method. The sensitivity analysis of weight changes for the two measures showed that the similarity measure based on distance was more stable than the similarity measure based on included angle in this application.

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Şenel, Güzide, Jeong-Gon Lee, and Kul Hur. "Distance and Similarity Measures for Octahedron Sets and Their Application to MCGDM Problems." Mathematics 8, no. 10 (2020): 1690. http://dx.doi.org/10.3390/math8101690.

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In this paper, in order to apply the concept of octahedron sets to multi-criteria group decision-making problems, we define several similarity and distance measures for octahedron sets. We present a multi-criteria group decision-making method with linguistic variables in octahedron set environment. We give a numerical example for multi-criteria group decision-making problems.

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Wang, Ju-Xiang. "A MAGDM Algorithm with Multi-Granular Probabilistic Linguistic Information." Symmetry 11, no. 2 (2019): 127. http://dx.doi.org/10.3390/sym11020127.

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The traditional multi-attribute group decision making (MAGDM) method needs to be improved to the integration of assessment information under multi-granular probabilistic linguistic environments. Some novel distance measures between two multi-granular probabilistic linguistic term sets (PLTSs) are proposed, and distance measures are proved to be reasonable. To calculate the weights of the alternative attributes, the extended cross-entropy method for multi-granular probabilistic linguistic term sets is proposed. Then, a novel extended MAGDM algorithm based on prospect theory (PT) is proposed. Two case studies of decision making (DM) on purchasing a car is provided to illustrate the application of the extended MAGDM algorithm. The case analyses are proposed to illustrate the novelty, feasibility, and application of the proposed MAGDM algorithm by comparing the other three algorithms based on TOPSIS, VIKOR, and Pang Qi et al.’s method. The analyses results demonstrate that the proposed algorithm based on PT is superior.

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Zhou, Huan, Jian-qiang Wang, and Hong-yu Zhang. "Multi-criteria decision-making approaches based on distance measures for linguistic hesitant fuzzy sets." Journal of the Operational Research Society 69, no. 5 (2018): 661–75. http://dx.doi.org/10.1080/01605682.2017.1400780.

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Peng, You, Yifang Tao, Boyi Wu, and Xiaoxin Wang. "Probabilistic Hesitant Intuitionistic Fuzzy Linguistic Term Sets and Their Application in Multiple Attribute Group Decision Making." Symmetry 12, no. 11 (2020): 1932. http://dx.doi.org/10.3390/sym12111932.

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Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology.

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Liu, Donghai, Yuanyuan Liu, and Lizhen Wang. "The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 4111–31. http://dx.doi.org/10.3233/jifs-200244.

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The linguistic q-rung orthopair fuzzy set is a powerful tool in representing linguistic assessments. Considering that the traditional decision making methods cannot deal with the situation that the best choice may not be the minimum or the maximum but between them, we propose an innovative TOPSIS method with linguistic q-rung orthopair fuzzy numbers based on the reference ideal theory. Firstly, the new operations of linguistic q-rung orthopair fuzzy sets are introduced based on the linguistic scale function. In addition, we propose the Minkowski distance measure of linguistic q-rung orthopair fuzzy numbers to make up for the defects of the existing distance measures based on the linguistic scale function. By using the new operations of linguistic q-rung orthopair fuzzy numbers, we propose the linguistic q-rung orthopair fuzzy weighted averaging operator and the linguistic q-rung orthopair fuzzy weighted geometric operator to aggregate linguistic decision information. Furthermore, we develop a reference ideal TOPSIS method to the linguistic q-rung orthopair fuzzy decision making problems. Finally, an example concerning the postgraduate entrance qualification assessment is given to illustrate the feasibility of the proposed method. Some comparative analysis is also given to show the efficiency of the method, in addition, the sensitivity analysis and stability analysis of the proposed method are also given.

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Hussain, Shahid, Zahid Hussain, Rashid Hussain, et al. "A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making." Axioms 13, no. 12 (2024): 858. https://doi.org/10.3390/axioms13120858.

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Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) and similarity (BP-similarity) until now. In this work, we propose a novel framework for the belief and plausibility of intuitionistic fuzzy sets (BP-IFSs) and their BP-distance and BP-similarity measures. We modified steps 4 and 5 of the classical TOPSIS method, utilizing both distance and similarity measures to rank the alternatives that satisfy all necessary axioms of distance and similarity. We present numerical examples involving pattern recognition, linguistic variables, and clustering to illustrate the efficiency of these measures, and we develop belief and plausibility TOPSIS (BP-TOPSIS) using the proposed criteria and apply it to complex multicriteria decision-making (MCDM) challenges. The results demonstrate the practicality and effectiveness of our approach.

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Faizi, Shahzad, Tabasam Rashid, Zeshui Xu, and Sohail Zafar. "Distance measures for hesitant intuitionistic fuzzy linguistic term sets based on a risk factor parameter." International Journal of Computers and Applications 41, no. 6 (2018): 418–35. http://dx.doi.org/10.1080/1206212x.2018.1465653.

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Liu, Donghai, Xiaohong Chen, and Dan Peng. "Distance Measures for Hesitant Fuzzy Linguistic Sets and Their Applications in Multiple Criteria Decision Making." International Journal of Fuzzy Systems 20, no. 7 (2018): 2111–21. http://dx.doi.org/10.1007/s40815-018-0460-0.

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Dziubalska-Kołaczyk, Katarzyna. "On the structure, survival and change of consonant clusters." Folia Linguistica 40, no. 1 (2019): 107–27. http://dx.doi.org/10.1515/flih-2019-0006.

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Abstract This paper shows how preferability measures can help to explain the cross-linguistic distribution of consonant clusters, their acquisition, as well as aspects of their diachronic development. Phonological preferability is measured in terms of cluster size and Net Auditory Distance, which interact with morphological complexity and frequency. Predictions derived from the preferability of clusters are tested against the evidence of language specific phonotactics, language use, language acquisition, psycholinguistic processing, and language change.

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Cui, Wenhua, and Jun Ye. "Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality." Symmetry 10, no. 8 (2018): 330. http://dx.doi.org/10.3390/sym10080330.

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Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs’ hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case.

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Wang, Yixin, and Jiang Jingyang. "Task-based explanation for genre effects: Evidence from a dependency treebank." PLOS ONE 18, no. 8 (2023): e0290381. http://dx.doi.org/10.1371/journal.pone.0290381.

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In task-based second language (L2) writing research, genre effects on linguistic features are usually explained by either task complexity hypothesis or differences in communicative demands. The basic distinction between the two explanations is determined by whether cognitive factors are at work. To date, the actual causes for L2 learners’ different linguistic features in different genres are still unclear. Aiming at providing empirical evidence for explaining the mechanism of genre effects, this investigation uses dependency-grammar-based measures to examine the role of cognitive factors in L2 argumentative, narrative, and descriptive writings. A total of 540 compositions from three different proficiency groups of English as a foreign language learners were collected, and their mean dependency distances and their distributions of dependency distance were calculated. It was found that in all proficiency groups of compositions, dependency distance distributions of five types showed significant differences between genres. Since dependency distance reflects cognitive load, those five dependency types were able to show that cognitive factors are at play in the writing process. Among the five types, the phrasal dependency relation types could reveal genre effects regardless of learners’ language proficiency, and clausal dependency relation types might pinpoint learners’ threshold of perceiving task complexity. The findings suggest that genre effects on linguistic features in L2 writings may result from different cognitive demand imposed by writing tasks with different genres, and genre effect may exhibit variation among different proficiency groups.

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Sharma, Dinesh K., Surender Singh, and Abdul Haseeb Ganie. "Distance-Based Knowledge Measure of Hesitant Fuzzy Linguistic Term Set With Its Application in Multi-Criteria Decision Making." International Journal of Fuzzy System Applications 11, no. 1 (2022): 1–20. http://dx.doi.org/10.4018/ijfsa.292460.

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Motivated by the structural aspect of the probabilistic entropy, the concept of fuzzy entropy enabled the researchers to investigate the uncertainty due to vague information. Fuzzy entropy measures the ambiguity/vagueness entailed in a fuzzy set. Hesitant fuzzy entropy and hesitant fuzzy linguistic term set based entropy presents a more comprehensive evaluation of vague information. In the vague situations of multiple-criteria decision-making, entropy measure is utilized to compute the objective weights of attributes. The weights obtained due to entropy measures are not reasonable in all the situations. To model such situation, a knowledge measure is very significant, which is a structural dual to entropy. A fuzzy knowledge measure determines the level of precision in a fuzzy set. This article introduces the concept of a knowledge measure for hesitant fuzzy linguistic term sets (HFLTS) and show how it may be derived from HFLTS distance measures. Authors also investigate its application in determining the weights of criteria in multi-criteria decision-making (MCDM).

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Zhang, Zhenyu, Jie Lin, Runsheng Miao, and Lixin Zhou. "Novel distance and similarity measures on hesitant fuzzy linguistic term sets with application to pattern recognition." Journal of Intelligent & Fuzzy Systems 37, no. 2 (2019): 2981–90. http://dx.doi.org/10.3233/jifs-190082.

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Hussain, Zahid, Sahar Abbas, and Miin-Shen Yang. "Distances and Similarity Measures of Q-Rung Orthopair Fuzzy Sets Based on the Hausdorff Metric with the Construction of Orthopair Fuzzy TODIM." Symmetry 14, no. 11 (2022): 2467. http://dx.doi.org/10.3390/sym14112467.

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In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM.

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Mattiussi, Claudio, Markus Waibel, and Dario Floreano. "Measures of Diversity for Populations and Distances Between Individuals with Highly Reorganizable Genomes." Evolutionary Computation 12, no. 4 (2004): 495–515. http://dx.doi.org/10.1162/1063656043138923.

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In this paper we address the problem of defining a measure of diversity for a population of individuals whose genome can be subjected to major reorganizations during the evolutionary process. To this end, we introduce a measure of diversity for populations of strings of variable length defined on a finite alphabet, and from this measure we derive a semi-metric distance between pairs of strings. The definitions are based on counting the number of substrings of the strings, considered first separately and then collectively. This approach is related to the concept of linguistic complexity, whose definition we generalize from single strings to populations. Using the substring count approach we also define a new kind of Tanimoto distance between strings. We show how to extend the approach to representations that are not based on strings and, in particular, to the tree-based representations used in the field of genetic programming. We describe how suffix trees can allow these measures and distances to be implemented with a computational cost that is linear in both space and time relative to the length of the strings and the size of the population. The definitions were devised to assess the diversity of populations having genomes of variable length and variable structure during evolutionary computation runs, but applications in quantitative genomics, proteomics, and pattern recognition can be also envisaged.

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Wei, Cuiping, Na Zhao, and Xijin Tang. "A Novel Linguistic Group Decision-Making Model Based on Extended Hesitant Fuzzy Linguistic Term Sets." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23, no. 03 (2015): 379–98. http://dx.doi.org/10.1142/s0218488515500166.

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Hesitant fuzzy linguistic term set (HFLTS) is a set with ordered consecutive linguistic terms, and is very useful in addressing the situations where people are hesitant in providing their linguistic assessments. Wang [H. Wang, Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, International Journal of Computational Intelligence Systems 8(1) (2015) 14–33.] removed the consecutive condition to introduce the notion of extended HFLTS (EHFLTS). The generalized form has wider applications in linguistic group decision-making. By introducing distance measures for EHFLTSs, in this paper we develop a novel multi-criteria group decision making model to deal with hesitant fuzzy linguistic information. The model collects group linguistic information by using EHFLTSs and avoids the possible loss of information. Moreover, it can assess the importance weights of criteria according to their subjective and objective information and rank alternatives based on the rationale of TOPSIS. In order to illustrate the applicability of the proposed algorithm, two examples are given and comparisons are made with the other existing methods.

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Tao, Zhifu, Bing Han, Huayou Chen, and Jiaming Zhu. "A new version of distance and similarity measures for hesitant fuzzy linguistic term sets and its application." Journal of Intelligent & Fuzzy Systems 34, no. 3 (2018): 1801–11. http://dx.doi.org/10.3233/jifs-16381.

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Wang, Xinxin, Zeshui Xu, Xunjie Gou, and Miao Xu. "Distance and Similarity Measures for Nested Probabilistic-Numerical Linguistic Term Sets Applied to Evaluation of Medical Treatment." International Journal of Fuzzy Systems 21, no. 5 (2019): 1306–29. http://dx.doi.org/10.1007/s40815-019-00625-x.

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Gou, Xunjie, Zeshui Xu, Huchang Liao, and Francisco Herrera. "Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment." Computers & Industrial Engineering 126 (December 2018): 516–30. http://dx.doi.org/10.1016/j.cie.2018.10.020.

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Zhang, Zhenyu, Jin Li, Youshuai Sun, and Jie Lin. "Novel Distance and Similarity Measures on Hesitant Fuzzy Linguistic Term Sets and Their Application in Clustering Analysis." IEEE Access 7 (2019): 100231–42. http://dx.doi.org/10.1109/access.2019.2927642.

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Holman, Eric W., Robert Walker, Taraka Rama, and Søren Wichmann. "Correlates of Reticulation in Linguistic Phylogenies." Language Dynamics and Change 1, no. 2 (2011): 205–40. http://dx.doi.org/10.1163/221058212x648072.

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AbstractThis paper discusses phylogenetic reticulation using linguistic data from the Automated Similarity Judgment Program or ASJP (Holman et al., 2008; Wichmann et al., 2010a). It contributes methodologically to the examination of two measures of reticulation in distance-based phylogenetic data, specifically the δ score of Holland et al. (2002) and the more recent Q-residuals of Gray et al. (2010). It is shown that the δ score is a more adequate measure of reticulation. Our empirical analyses examine possible correlations between δ and (a) the size (number of languages), (b) age, and (c) heterogeneity of language groups, (d) linguistic isolation of individual languages within their respective phylogenies, and (e) the status of speech forms as dialects or recently emerged languages. Among these, only (d) is significantly correlated with δ. Our interpretation is that δ is a realistic measure of reticulation and sensitive to effects of socio-historical events such as language extinction. Finally, we correlate average δ scores for different language families with the goodness of fit between ASJP and expert classifications, showing that the δ scores explain much of the variance.

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Becker, Anke, Benjamin Enke, and Armin Falk. "Ancient Origins of the Global Variation in Economic Preferences." AEA Papers and Proceedings 110 (May 1, 2020): 319–23. http://dx.doi.org/10.1257/pandp.20201071.

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This paper shows that contemporary population-level heterogeneity in risk aversion, time preference, altruism, positive reciprocity, negative reciprocity, and trust partly traces back to the structure of the migration patterns of our very early ancestors. To document this pattern, we link differences in preferences between populations to the length of time elapsed since the ancestors of the respective groups broke apart from each other, as proxied by genetic and linguistic distance measures. Preference differences are significantly increasing in ancestral distance in both cross-country regressions and within-country analyses across groups of migrants.

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Lacsina, Nadine, and Aiden Yeh. "Keep social distance: The linguistic landscape of the major malls in Jeddah amid the COVID-19 pandemic." Topics in Linguistics 23, no. 1 (2022): 39–61. http://dx.doi.org/10.2478/topling-2022-0004.

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Abstract This study examines the linguistic landscape of the two major malls in Jeddah, Kingdom of Saudi Arabia, through social distancing posters and signs during the COVID-19 pandemic. The study draws on the conceptual framework of linguistic landscape theory, speech acts and semiotics to unveil language dominance, linguistic messages, image-text relations and poster elements that enforce social distancing. A survey questionnaire, primarily aimed at expats, was also administered to find out how they view and interpret the use of bilingual modes in disseminating the social distancing measures. The semiotic analysis reveals that Arabic and English are used in most of the posters, but Arabic remains the dominant language and the preferred medium of information dissemination. Speech acts analysis shows that representatives and directives facilitate implementation of social distancing. The findings also suggest that semiotic modes and signifiers (inscription and materiality) reinforce the effectiveness of the posters. Overall, the use of Arabic and English reflects the country’s stance on language policy and economic vision for Jeddah to be a truly global city amid the pandemic.

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Zhang, Junling, Ying Hong, Xiaowen Qi, and Changyong Liang. "Probabilistic Hybrid Linguistic Approaches for Multiple Attribute Group Decision Making with Decision Hesitancy and the Prioritization of Attribute Relationships." Symmetry 12, no. 2 (2020): 235. http://dx.doi.org/10.3390/sym12020235.

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Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches.

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Gill, A., and C. R. Bector. "A fuzzy linguistic approach to data quantification and construction of distance measures for the part family formation problem." International Journal of Production Research 35, no. 9 (1997): 2565–78. http://dx.doi.org/10.1080/002075497194660.

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Liao, Huchang, Zeshui Xu, and Xiao-Jun Zeng. "Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making." Information Sciences 271 (July 2014): 125–42. http://dx.doi.org/10.1016/j.ins.2014.02.125.

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Baranov, Victor A. "Distributive Dictionary of the Historical Corpus “Manuscript”: Problem Statement, Material, Methods." Current Issues in Philology and Pedagogical Linguistics, no. 2 (June 25, 2022): 94–106. http://dx.doi.org/10.29025/2079-6021-2022-2-94-106.

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Characteristics of linguistic materials and methods used to create an electronic distributive dictionary based on the historical corpus “Manuscript” (http://manuscripts.ru/mns/mns_evp.vec.main ), containing marked–up machine-readable transcriptions of extant Slavonic manuscripts and excerpts of the X-XV centuries, are given. The conditions for the use of statistical methods for the distributive analysis of the words of ancient Slavonic texts are discussed, the requirements for specialized tools and demonstration of the forms of visualization of the prototype of the dictionary are formulated. Examples of methods of automatic extraction of words with similar lexical environment from a large array of text data are given. The procedures and tools for preparing linguistic data are described (in particular, the formation of subcorps based on metadata and the methods implemented in the n-gram module for extracting the most frequent combinations of linguistic units from the corpus), the use of the k-skip-n-gram method for calculating word vectors and the method of finding the cosine distance between vectors is justified. The parameters of the dictionary query form are demonstrated, it allows specifying the type of the analyzed linguistic unit (lemma or text precedent), its mask and the cosine distance threshold. An example of a sample for the lemma лѣто ‘summer’ is given, it includes a list of words that have the closest contextual compatibility, the values of the cosine distances of the analyzed and the words close in distribution, as well as a list of words that occur next to the analyzed and the searched words. A sampling graph is shown, it demonstrates not only semantic, thematic, associative analogues of the word лѣто ‘summer’, but also some groups of associates. The analysis of the material, methods and results allowed us to draw conclusions about the need to use statistical measures when assessing the proximity of their components for the formation of vectors and about some other conditions for preprocessing linguistic material.

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Razak, Samsiah Abdul, Zahari Md Rodzi, Faisal Al-Sharqi, and Nazirah Ramli. "Revolutionizing Decision-Making in E-Commerce and IT Procurement: An IVPNS-COBRA Linguistic Variable Framework for Enhanced Multi-Criteria Analysis." International Journal of Economic Sciences 14, no. 1 (2025): 1–31. https://doi.org/10.31181/ijes1412025176.

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Real-world challenges in e-commerce strategy selection and IT supplier evaluation are inherently complex due to uncertainty and incomplete information, necessitating a multi-faceted approach for effective decision-making. Traditional single methods often fail to address these complexities adequately. To overcome this limitation, this research introduces an advanced methodology by integrating the Interval-Valued Pythagorean Neutrosophic Set (IVPNS) with the Comprehensive Distance-Based Ranking (COBRA) approach, enhancing the handling of indeterminate information related to truth, falsity, and uncertainty. IVPNS provides a robust mathematical framework for managing ambiguity, a common challenge in Multi-Criteria Decision-Making (MCDM) across various domains. Prior to this study, IVPNS lacked a linguistic variable—a crucial component for expressing human judgments. To bridge this gap, we enhance the IVPNS-COBRA framework by incorporating 5-point and 7-point linguistic scales, ensuring compliance with established IVPNS conditions. Additionally, we introduce two distance measures, Euclidean and Hamming distances, to refine alternative evaluations. The proposed IVPNS-COBRA method is validated through real-world applications, including the evaluation of three e-commerce development strategies (assessed against five criteria) and four IT supplier selection alternatives (evaluated using nine criteria). The results demonstrate the reliability of this MCDM model, providing decision-makers with a more precise and structured approach for selecting optimal e-commerce strategies and IT suppliers in complex environments.

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Montemagni, Simonetta. "The Space of Tuscan Dialectal Variation: A Correlation Study." International Journal of Humanities and Arts Computing 2, no. 1-2 (2008): 135–52. http://dx.doi.org/10.3366/e1753854809000354.

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The paper illustrates the results of a correlation study focusing on linguistic variation in an Italian region, Tuscany. By exploiting a multi-level representation scheme of dialectal data, the study analyses attested patterns of phonetic and morpho-lexical variation with the aim of testing the degree of correlation between a) phonetic and morpho-lexical variation, and b) linguistic variation and geographic distance. The correlation analysis was performed by combining two complementary approaches proposed in dialectometric literature, namely by computing both global and place-specific correlation measures and by inspecting their spatial distribution. Achieved results demonstrate that phonetic and morpho-lexical variations in Tuscany seem to follow a different pattern than encountered in previous studies.

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Zeng, Shouzhen, Tomas Baležentis, and Chonghui Zhang. "A Method Based on OWA Operator and Distance Measures for Multiple Attribute Decision Making with 2-Tuple Linguistic Information." Informatica 23, no. 4 (2012): 665–81. http://dx.doi.org/10.15388/informatica.2012.380.

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